Notes

Journal of Mathematical Chemistry

, Volume 2, Issue 3, pp 267-277

First online:

How to compute the Wiener index of a graph

  • Bojan MoharAffiliated withDepartment of Ma theima tics, University E.K. of LjubljanaDepartment of Mathematics and Statistics, Simon Fraser University
  • , Tomaž PisanskiAffiliated withDepartment of Ma theima tics, University E.K. of LjubljanaDepartment of Mathematics and Statistics, Simon Fraser University

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Abstract

The Wiener index of a graphG is equal to the sum of distances between all pairs of vertices ofG. It is known that the Wiener index of a molecular graph correlates with certain physical and chemical properties of a molecule. In the mathematical literature, many good algorithms can be found to compute the distances in a graph, and these can easily be adapted for the calculation of the Wiener index. An algorithm that calculates the Wiener index of a tree in linear time is given. It improves an algorithm of Canfield, Robinson and Rouvray. The question remains: is there an algorithm for general graphs that would calculate the Wiener index without calculating the distance matrix? Another algorithm that calculates this index for an arbitrary graph is given.